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This subject aims to provide students with grounding in advanced financial mathematics, covering option pricing under the binomial model; risk‐neutral pricing of derivative securities; Brownian motion; introduction to Itô΄ formula and SDEs; stochas asset models; Black‐Scholes model; arbitrage and hedging; interest‐rate models; actuarial applications and simple models for credit risk.
Intended learning outcomes
On successful completion of this subject a student should be able to:
- Demonstrate a knowledge of the properties of option prices, valuation methods and hedging techniques, and be able to apply these;
- Show how to use binomial trees and lattices in valuing options;
- Apply the Ito calculus;
- Derive option prices under the Black-Scholes model;
- Describe and apply in simple models, including the binomial model and the Black-Scholes model, the approach to pricing using deflators and demonstrate its equivalence to the risk-neutral pricing approach;
- Demonstrate a knowledge of models of the term structure of interest rates;
- Describe, as a computational tool, the risk-neutral approach to the pricing of zero coupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest;
- Demonstrate a knowledge of simple models for credit risk.
High level of development:
- Written communication;
- Problem solving;
- Mathematical reasoning;
- Simple models of credit risk;
- Application of theory to practice;
- Interpretation and analysis.
Last updated: 31 January 2024